Technology Anxiety In a 2018 survey conducted by Northeastern University, 28 % of working adults with education levels less than a bachelor’s degree worried that their job would be eliminated due to new technology or automation. This was based on a 95 % confidence interval with a margin of error of 3 percentage points. a. Report the confidence interval for the proportion of adults with education level less than a bachelor’s degree who are worried about job loss due to new technology or automation. b. If the sample size were smaller and the sample proportion stayed the same, would the resulting interval be wider or narrower than the one obtained in part a? c. If the confidence level were 99 % rather than 95 % and the sample proportion stayed the same, would the interval be wider or narrower than the one obtained in part a? d. In 2018 the population of the United States was roughly 327 million. If 50 million people were added to the population what effect, if any, would this have on the intervals obtained in this problem?
Technology Anxiety In a 2018 survey conducted by Northeastern University, 28 % of working adults with education levels less than a bachelor’s degree worried that their job would be eliminated due to new technology or automation. This was based on a 95 % confidence interval with a margin of error of 3 percentage points. a. Report the confidence interval for the proportion of adults with education level less than a bachelor’s degree who are worried about job loss due to new technology or automation. b. If the sample size were smaller and the sample proportion stayed the same, would the resulting interval be wider or narrower than the one obtained in part a? c. If the confidence level were 99 % rather than 95 % and the sample proportion stayed the same, would the interval be wider or narrower than the one obtained in part a? d. In 2018 the population of the United States was roughly 327 million. If 50 million people were added to the population what effect, if any, would this have on the intervals obtained in this problem?
Solution Summary: The author explains how the confidence interval for the population proportion is (0.25,0.31).
Technology Anxiety In a 2018 survey conducted by Northeastern University,
28
%
of working adults with education levels less than a bachelor’s degree worried that their job would be eliminated due to new technology or automation. This was based on a
95
%
confidence interval with a margin of error of 3 percentage points.
a. Report the confidence interval for the proportion of adults with education level less than a bachelor’s degree who are worried about job loss due to new technology or automation.
b. If the sample size were smaller and the sample proportion stayed the same, would the resulting interval be wider or narrower than the one obtained in part a?
c. If the confidence level were
99
%
rather than
95
%
and the sample proportion stayed the same, would the interval be wider or narrower than the one obtained in part a?
d. In 2018 the population of the United States was roughly 327 million. If 50 million people were added to the population what effect, if any, would this have on the intervals obtained in this problem?
Definition Definition Number of subjects or observations included in a study. A large sample size typically provides more reliable results and better representation of the population. As sample size and width of confidence interval are inversely related, if the sample size is increased, the width of the confidence interval decreases.
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Part (b)
Draw a scatter plot of the ordered pairs.
N
Life
Expectancy
Life
Expectancy
80
70
600
50
40
30
20
10
Year of
1950
1970 1990
2010 Birth
O
Life
Expectancy
Part (c)
800
70
60
50
40
30
20
10
1950
1970 1990
W
ALT
林
$
#
4
R
J7
Year of
2010 Birth
F6
4+
80
70
60
50
40
30
20
10
Year of
1950 1970 1990
2010 Birth
Life
Expectancy
Ox
800
70
60
50
40
30
20
10
Year of
1950 1970 1990 2010 Birth
hp
P.B.
KA
&
7
80
% 5
H
A
B
F10
711
N
M
K
744
PRT SC
ALT
CTRL
Harvard University
California Institute of Technology
Massachusetts Institute of Technology
Stanford University
Princeton University
University of Cambridge
University of Oxford
University of California, Berkeley
Imperial College London
Yale University
University of California, Los Angeles
University of Chicago
Johns Hopkins University
Cornell University
ETH Zurich
University of Michigan
University of Toronto
Columbia University
University of Pennsylvania
Carnegie Mellon University
University of Hong Kong
University College London
University of Washington
Duke University
Northwestern University
University of Tokyo
Georgia Institute of Technology
Pohang University of Science and Technology
University of California, Santa Barbara
University of British Columbia
University of North Carolina at Chapel Hill
University of California, San Diego
University of Illinois at Urbana-Champaign
National University of Singapore
McGill…
Name
Harvard University
California Institute of Technology
Massachusetts Institute of Technology
Stanford University
Princeton University
University of Cambridge
University of Oxford
University of California, Berkeley
Imperial College London
Yale University
University of California, Los Angeles
University of Chicago
Johns Hopkins University
Cornell University
ETH Zurich
University of Michigan
University of Toronto
Columbia University
University of Pennsylvania
Carnegie Mellon University
University of Hong Kong
University College London
University of Washington
Duke University
Northwestern University
University of Tokyo
Georgia Institute of Technology
Pohang University of Science and Technology
University of California, Santa Barbara
University of British Columbia
University of North Carolina at Chapel Hill
University of California, San Diego
University of Illinois at Urbana-Champaign
National University of Singapore…
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Hypothesis Testing - Solving Problems With Proportions; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=76VruarGn2Q;License: Standard YouTube License, CC-BY
Hypothesis Testing and Confidence Intervals (FRM Part 1 – Book 2 – Chapter 5); Author: Analystprep;https://www.youtube.com/watch?v=vth3yZIUlGQ;License: Standard YouTube License, CC-BY